void test(Matrix& A, const char* name)
{
using mtl::irange;
A= 0.0;
A[0][0]= 1.0;
hessian_setup(A, 1.0);
A[irange(0, 8)][irange(0, 8)];
mtl::matrix::recursator<Matrix> rec(A);
std::cout << "\n" << name << "\n";
std::cout << "A:\n" << A << '\n';
std::cout << "A[irange(0, 8)][irange(0, 8)]:\n" << A[irange(0, 8)][irange(0, 8)] << '\n';
std::cout << "*rec:\n" << *rec << '\n';
mtl::matrix::recursator<Matrix> nw= north_west(rec);
std::cout << "north_west:\n" << *nw << '\n';
std::cout << "north_west of north_west:\n" << *north_west(nw) << '\n';
MTL_THROW_IF((*north_west(nw))[0][0] != 0.0, mtl::runtime_error("(*north_west(nw))[0][0] != 0.0"));
(*north_west(nw))[0][0]= 2.0;
std::cout << "south_east of north_west:\n" << *south_east(nw) << '\n';
MTL_THROW_IF((*south_east(nw))[0][0] != 4.0, mtl::runtime_error("(*south_east(nw))[0][0] != 4.0"));
std::cout << "north_west of north_west:\n" << *north_west(nw) << '\n';
MTL_THROW_IF((*north_west(nw))[0][0] != 2.0, mtl::runtime_error("(*north_west(nw))[0][0] != 2.0"));
std::cout << "south_east of north_west:\n" << *south_east(nw) << '\n';
MTL_THROW_IF((*south_east(nw))[0][0] != 4.0, mtl::runtime_error("(*south_east(nw))[0][0] != 4.0"));
std::cout << "nw.first_address() == " << nw.first_address()
<< ", &(*nw)[0][0] == " << &(*nw)[0][0] << '\n';
MTL_THROW_IF(nw.first_address() != &(*nw)[0][0], mtl::runtime_error("Inconsistency in address calculation"));
}
void test2(Matrix& A, const char* name)
{
using mtl::irange; using mtl::imax; using mtl::iall;
A= 0.0;
A[1][1]= 1.0;
hessian_setup(A, 1.0);
std::cout << "\n" << name << "\nA == \n" << A;
cout << "A[irange(2, 4)][irange(2, imax)] == \n"
<< A[irange(2, 4)][irange(2, imax)] << "\n";
Matrix B(A[irange(2, 4)][irange(2, imax)]);
MTL_THROW_IF(B[0][0] != 4.0, mtl::runtime_error("Wrong value in B"));
MTL_THROW_IF(A[irange(2, 4)][irange(2, imax)][0][0] != 4.0, mtl::runtime_error("Wrong value in A[][]"));
Matrix C(A[irange(4, imax)][irange(0, imax)]);
std::cout << "\n" << name << "\nA[irange(4, imax)][irange(0, imax)] == \n" << C;
MTL_THROW_IF(C[0][1] != 5.0, mtl::runtime_error("Wrong value in C"));
Matrix D(A[irange(4, imax)][iall]);
std::cout << "\n" << name << "\nA[irange(4, imax)][iall] == \n" << C;
MTL_THROW_IF(D[0][1] != 5.0, mtl::runtime_error("Wrong value in D"));
}
int bicgstab_ell(const LinearOperator &A, Vector &x, const Vector &b,
const LeftPreconditioner &L, const RightPreconditioner &R,
Iteration& iter, size_t l)
{
mtl::vampir_trace<7006> tracer;
using mtl::size; using mtl::irange; using mtl::imax; using mtl::matrix::strict_upper;
typedef typename mtl::Collection<Vector>::value_type Scalar;
typedef typename mtl::Collection<Vector>::size_type Size;
if (size(b) == 0) throw mtl::logic_error("empty rhs vector");
const Scalar zero= math::zero(Scalar()), one= math::one(Scalar());
Vector x0(resource(x)), y(resource(x));
mtl::vector::dense_vector<Vector> r_hat(l+1,Vector(resource(x))), u_hat(l+1,Vector(resource(x)));
// shift problem
x0= zero;
r_hat[0]= b;
if (two_norm(x) != zero) {
r_hat[0]-= A * x;
x0= x;
x= zero;
}
Vector r0_tilde(r_hat[0]/two_norm(r_hat[0]));
y= solve(L, r_hat[0]);
r_hat[0]= y;
u_hat[0]= zero;
Scalar rho_0(one), rho_1(zero), alpha(zero), Gamma(zero), beta(zero), omega(one);
mtl::matrix::dense2D<Scalar> tau(l+1, l+1);
mtl::vector::dense_vector<Scalar> sigma(l+1), gamma(l+1), gamma_a(l+1), gamma_aa(l+1);
while (! iter.finished(r_hat[0])) {
++iter;
rho_0= -omega * rho_0;
for (Size j= 0; j < l; ++j) {
rho_1= dot(r0_tilde, r_hat[j]);
beta= alpha * rho_1/rho_0; rho_0= rho_1;
for (Size i= 0; i <= j; ++i)
u_hat[i]= r_hat[i] - beta * u_hat[i];
y= A * Vector(solve(R, u_hat[j]));
u_hat[j+1]= solve(L, y);
Gamma= dot(r0_tilde, u_hat[j+1]);
alpha= rho_0 / Gamma;
for (Size i= 0; i <= j; ++i)
r_hat[i]-= alpha * u_hat[i+1];
if (iter.finished(r_hat[j])) {
x= solve(R, x);
x+= x0;
return iter;
}
r_hat[j+1]= solve(R, r_hat[j]);
y= A * r_hat[j+1];
r_hat[j+1]= solve(L, y);
x+= alpha * u_hat[0];
}
// mod GS (MR part)
irange i1m(1, imax);
mtl::vector::dense_vector<Vector> r_hat_tail(r_hat[i1m]);
tau[i1m][i1m]= orthogonalize_factors(r_hat_tail);
for (Size j= 1; j <= l; ++j)
gamma_a[j]= dot(r_hat[j], r_hat[0]) / tau[j][j];
gamma[l]= gamma_a[l]; omega= gamma[l];
if (omega == zero) return iter.fail(3, "bicg breakdown #2");
// is this something like a tri-solve?
for (Size j= l-1; j > 0; --j) {
Scalar sum= zero;
for (Size i=j+1;i<=l;++i)
sum += tau[j][i] * gamma[i];
gamma[j] = gamma_a[j] - sum;
}
gamma_aa[irange(1, l)]= strict_upper(tau[irange(1, l)][irange(1, l)]) * gamma[irange(2, l+1)] + gamma[irange(2, l+1)];
x+= gamma[1] * r_hat[0];
r_hat[0]-= gamma_a[l] * r_hat[l];
u_hat[0]-= gamma[l] * u_hat[l];
for (Size j=1; j < l; ++j) {
u_hat[0] -= gamma[j] * u_hat[j];
x+= gamma_aa[j] * r_hat[j];
r_hat[0] -= gamma_a[j] * r_hat[j];
}
}
x= solve(R, x); x+= x0; // convert to real solution and undo shift
return iter;
}